A new model for oscillations in the peroxidase-oxidase reaction

Complex dynamics in an unexplored simple model of the peroxidase-oxidase reaction

A previously overlooked version of the so-called Olsen model of the peroxidase-oxidase reaction has been studied numerically using 2D isospike stability and maximum Lyapunov exponent diagrams and reveals a rich variety of dynamic behaviors not observed before. The model has a complex bifurcation structure involving mixed-mode and bursting oscillations as well as quasiperiodic and chaotic dynamics. In addition, multiple periodic and non-periodic attractors coexist for the same parameters. For some parameter values, the model also reveals formation of mosaic patterns of complex dynamic states. The complex dynamic behaviors exhibited by this model are compared to those of another version of the same model, which has been studied in more detail. The two models show similarities, but also notable differences between them, e.g., the organization of mixed-mode oscillations in parameter space and the relative abundance of quasiperiodic and chaotic oscillations. In both models, domains with chaotic dynamics contain apparently disorganized subdomains of periodic attractors with dinoflagellate-like structures, while the domains with mainly quasiperiodic behavior contain subdomains with periodic attractors organized as regular filamentous structures. These periodic attractors seem to be organized according to Stern-Brocot arithmetics. Finally, it appears that toroidal (quasiperiodic) attractors develop into first wrinkled and then fractal tori before they break down to chaotic attractors.

Feedback loops for Shil’nikov chaos: The peroxidase-oxidase reaction

Special structures in a chemical reaction network can give rise to bistability, oscillations, and chaos. It has been shown recently [A. Sensse and M. Eiswirth, J. Chem. Phys. 122, 044516 (2005)] that the introduction of an additional species in a supplementary feedback loop to a minimal autocatalytic oscillator gives rise to chaotic dynamics in a certain range of parameters, independent of the particular realization of the additional loop. This provides a possibility to decide if chaos may occur just by analyzing the network structure of an existing model. Here, we apply this concept to analyze the complex dynamics in several essential subsystems of the peroxidase-oxidase reaction system. The aim of the present paper is to determine the nature of the occurring chaos and its location in the parameter space by numerical bifurcation analysis and simulations.

Oscillations in the peroxidase-oxidase reaction: a comparison of different peroxidases

The nonlinear behavior of the peroxidase-oxidase reaction was studied using structurally different peroxidases. For the first time sustained oscillations with peroxidases other than horseradish peroxidase in a single-enzyme system were observed. All peroxidases that showed significant oxidase activity were able to generate sustained oscillations. When adjusting the overall reaction rate, either of the two modifiers 2,4-dichlorophenol or Methylene blue could be omitted from the reaction. Due to the observation of different enzyme intermediates when using different peroxidases, we conclude that the mechanisms responsible for oscillatory kinetics may vary from one peroxidase to the other.

A hydrogen peroxide assay based on the peroxidase-oxidase reaction. Numerical simulation of the reaction mechanism

In order to explain an assay method for H2O2, based on the horseradish peroxidase/NADH/H2O2 system, we performed a numerical simulation of this complex reaction mechanism. For this purpose, we applied a simplified version of a model designed by Yokota and Yamazaki to our experimental conditions [Yokota, K. & Yamazaki, I. (1977) Biochemistry 16, 1913-1918]. This modification leads to a kinetic behaviour of the system very similar to our experimental results when the presence of superoxide dismutase is simulated. These simulations confirm that hydrogen peroxide concentrations are proportional to the total amount of NADH oxidized. We also showed that superoxide dismutase activity can be determined by this assay method. Moreover, in samples containing superoxide dismutase and hydrogen peroxide, the simulations showed that both superoxide dismutase and hydrogen peroxide can be determined using our assay method.